Time-averaged MSD of Brownian motion

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution

The use of information and communication technologies by portuguese teachers

We present a study made in Portugal, in 2001/2002, on the use of Information and Communication Technologies (ICT) by teachers of all teaching levels (except high education), in both public and private schools. It was an initiative of the Ministry of Education (“Nonio – 21st Century” program), which was carried out by the Competence Centre “Softsciences” and the Centre for Computational Physics of the University of Coimbra. Some of the conclusions of this study, that has collected data from 19337 teachers, are the following: the majority of Portuguese teachers own a PC and approximately half of them use it in several activities, though their use of computers with students is limited. Primary school teachers use often the PC in their schools, though, probably, in an incipient way. The self-training of teachers in ICT is quite common. The Internet is more used by 3rd cycle (last part of middle school) and high school teachers, being most of its users male and young. These and other conclusions should be taken into account in a strategy towards incrementing a better use of new technologies in schools. The whole study is available in: http://nautilus.fid.uc.pt/cec/estud

Phonon Universal Transmission Fluctuations and Localization in Semiconductor Superlattices with a Controlled Degree of Order

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks- Teller superlattice exhibits a transition from periodic ordering, with alterna- ting layers, to the phase separated opposite limit; including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any $N$ conse- cutive layers) and long range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a {\it universal\/} curve irrespective of the specific type of disorder of the SL. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal transmission fluctuations.Comment: 16-pages, Revte

Ethyl 6-(4-chloro­phen­yl)-4-(4-methoxy­phen­yl)-2-oxocyclo­hex-3-ene-1-carboxyl­ate

In the title compound, C22H21ClO4, the cyclo­hex-3-ene unit adopts an envelope conformation in both independent mol­ecules comprising the asymmetric unit. The two benzene rings are inclined to each other at a dihedral angle of 82.03 (5)° [86.37 (5)°]. In the crystal, the molecules interact via C—H⋯O, C—H⋯Cl and C—H⋯π interactions

Dephasing by a Continuous-Time Random Walk Process

Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like , where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to be studied within a single framework. We apply the results to extract qubit-lattice interaction parameters from dephasing data of P-doped Si semiconductors (data collected elsewhere), and to calculate the two-dimensional spectrum of a three level harmonic oscillator undergoing random frequency modulations.Comment: 25 pages, 4 figure

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature

A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic dimension cause an explosion of the computational effort. We propose and analyze a multilevel version of the stochastic collocation method that, as is the case for multilevel Monte Carlo (MLMC) methods, uses hierarchies of spatial approximations to reduce the overall computational complexity. In addition, our proposed approach utilizes, for approximation in stochastic space, a sequence of multi-dimensional interpolants of increasing fidelity which can then be used for approximating statistics of the solution as well as for building high-order surrogates featuring faster convergence rates. A rigorous convergence and computational cost analysis of the new multilevel stochastic collocation method is provided, demonstrating its advantages compared to standard single-level stochastic collocation approximations as well as MLMC methods. Numerical results are provided that illustrate the theory and the effectiveness of the new multilevel method

Towards operational use of aircraft‐derived observations: a case study at London Heathrow airport

Mode-Selective Enhanced Surveillance (Mode-S EHS) aircraft reports can be collected at a low-cost, and are readily available around busy airports. The new work presented here demonstrates that observations derived from Mode-S EHS reports can be used to study the evolution of temperature inversions since the data have a high spatial and temporal frequency. This is illustrated by a case study centred around London Heathrow airport for the period 4 to 5 January 2015. Using Mode-S EHS reports from multiple aircraft and after applying quality control criteria, vertical temperature profiles are constructed by aggregating these reports at discrete intervals between the surface and 3000m. To improve these derived temperatures, four smoothing methods using low-pass filters are evaluated. The effect of smoothing reduces the variance in the aircraft derived temperature by approximately half. After smoothing, the temperature variance between the altitudes 3000m and 1000m is 1K to 2K; and below 1000m it is 2K to 4K. While the differences between the four smoothing methods are small, exponential smoothing is favoured because it uses all available Mode-S EHS reports. The resulting vertical profiles may be useful in operational meteorology for identifying elevated temperature inversions above 1000m. However, below 1000m they are less useful because of the reduced precision of the reported Mach number. A better source of in situ temperature observations would be for aircraft to use the meteorological reporting function of their automatic dependent surveillance (ADS) system